1. The Fish and Game Department in Wisconsin stocked a new lake with the followi
ID: 3245105 • Letter: 1
Question
1. The Fish and Game Department in Wisconsin stocked a new lake with the following distribution of game fish. After five years a random sample of 225 fish from the lake were netted, identified, and released The Initial Stocking Distribution and Sample Distribution after 5 years are shown in the following table. The Fish and Game Department want to determine if the sample distribution of fish in the lake after six years fits the initial stocking distribution. Use a chi-square hypothesis test to answer their question; us a 5% level of significance. (DO NOT ROUND YOUR CALCULATIONS- USE 4 DECIMAL PLACES) Initial Stocking Distribution after 5 OBSERVED: Sample Distribution EXPECTED (O - E)2 FISH (O-E) (O-E years Pike Trout Perch 10% 15% 20% 25% 30% 40 20 38 Bass 62 Bluegill 65 100% 225 225 (a) State the null and alternate hypotheses and the level of significance (b) Find the critical value(s). Sketch the sampling distribution and show the area corresponding to the critical value (c) Calculate the sample test statistic from the table above. Find the P-value of your test.Explanation / Answer
a) null hypothesis:sample distribution of fish in the lake after six years fits intiial stocking distribution
alternate hypothesis:sample distribution of fish in the lake after six years does not fits intiial stocking distribution
b)critical value at 5% level of signficance and (n-1=4) degree of freedom =9.4877
c)
here test stat =20.9822
p value =0.0003
d) as p value is less then 0.05 level of significance ; we reject null hypothesis,
we have sufficient evidence to conclude that sample distribution of fish in the lake after six years does not fits intiial stocking distribution
Initial stock observed Expected Chi square fish Distribution O E=total*p (O-E) (O-E)^2 =(O-E)^2/E pike 10% 40.000 22.50 17.50 306.25 13.61 trout 15% 20.000 33.75 -13.75 189.06 5.60 Perch 20% 38.000 45.00 -7.00 49.00 1.09 bass 25% 62.000 56.25 5.75 33.06 0.59 bluegill 30% 65.000 67.50 -2.50 6.25 0.09 100% 225 225 0 20.9822Related Questions
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